Paulo Carrillo Rouse

A Schwartz type algebra for the Tangent groupoid

We investigate when Isomorphism Conjectures, such as the ones due to Baum-Connes, Bost and Farrell-Jones, are stable under colimits of groups over directed sets (with not necessarily injective structure maps). We show in particular that both the K-theoretic Farrell-Jones Conjecture and the Bost Conjecture with coefficients hold for those groups for which Higson, Lafforgue and Skandalis have disproved the Baum-Connes Conjecture with coefficients.We present a

Higher localized analytic indices and strict deformation quantization

C^*

Geometric obstructions for Fredholm boundary conditions for manifolds with corners

-algebra which is naturally associated to the

A cohomological formula for the Atiyah–Patodi–Singer index on manifolds with boundary

ax+b

Compactly supported analytic indices for Lie groupoids

-semigroup over

Twisted longitudinal index theorem for foliations and wrong way functoriality

\mathbb N

Multiplicative structures and the twisted Baum-Connes assembly map

. It is simple and purely infinite and can be obtained from the algebra considered by Bost and Connes by adding one unitary generator which corresponds to addition. Its stabilization can be described as a crossed product of the algebra of continuous functions, vanishing at infinity, on the space of finite adeles for

Twisted index theory for foliations

\mathbb Q

The Atiyah-Singer cobordism invariance and the tangent groupoid

by the natural action of the

Longitudinal b-operators, Blups and Index theorems

ax+b